Recently, right-angled Artin groups have attracted much attention in geometric group theory.
They have a rich structure of subgroups and nice algorithmic properties, and they give rise to …

The key idea in geometric group theory is to study infinite groups by endowing them with a
metric and treating them as geometric spaces. This applies to many groups naturally …

We provide new examples of acylindrically hyperbolic groups arising from actions on
simplicial trees. In particular, we consider amalgamated products and HNN-extensions, one …

We study the geometry of non-relatively hyperbolic groups. Generalizing a result of
Schwartz, any quasi-isometric image of a non-relatively hyperbolic space in a relatively …

A graph is Helly if every family of pairwise intersecting combinatorial balls has a nonempty
intersection. We show that weak Garside groups of finite type and FC-type Artin groups are …

The rank of a hierarchically hyperbolic space is the maximal number of unbounded factors in
a standard product region. For hierarchically hyperbolic groups, this coincides with the …

In this article we survey recent progress on quasi-isometric rigidity of polycyclic groups.
These results are contributions to Gromov's program for classifying finitely generated groups …

The notion of thickness, introduced in (Math. Ann. 344 (2009) 543–595), is one of the first
tools developed to study the quasi-isometric behavior of weakly relatively hyperbolic groups …

arXiv:1205.0202v3 [math.GT] 24 Apr 2013 Page 1 arXiv:1205.0202v3 [math.GT] 24 Apr 2013
3-MANIFOLD GROUPS MATTHIAS ASCHENBRENNER, STEFAN FRIEDL, AND HENRY …

Let $ G $ be a right-angled Artin group with $|\mathrm {Out}(G)|<+\infty $. We prove that if a
countable group $ H $ with bounded torsion is measure equivalent to $ G $, with an $ L^ 1 …